The present invention relates to the field of digital modulated radio signals and more particularly to a method for the implementation of a non-coherent sequence estimation receiver for linear digital modulations.
In the relevant technical field, there are different classes of receivers. A first class of receivers is based on the structure of an optimum coherent receiver, that is, a receiver that minimizes the error probability on decided symbols when the synchronism is perfectly known, and in particular, the phase of the received signal, which will be dealt with hereafter. The implementation of such a receiver does not exhibit particular problems in a laboratory environment, where the modulation carrier is always available, but it cannot be followed up in practice when this receiver is placed in the field and the carrier is not available. In these cases, a preferred solution is to supply the receiver with a synchronization device enabling it to xe2x80x9crecoverxe2x80x9d the information on the phase of the modulated carrier. The devices often used for this purpose are phase locked loops (Phase Locked Loop, or PLL). Such a receiver shall be hereinafter referred to as xe2x80x9cpseudocoherentxe2x80x9d, since it is implemented according to the configuration of a coherent receiver to which a phase reference is supplied by a synchronization device. In these receivers, the phase is recovered but for multiples of 2xcfx80/n, where n depends on the type of adopted modulation. As a consequence of the ambiguity in the phase introduced by the PLL, a differential encoding must be used in transmission, that is a coding where the information is not associated with the absolute phase of the modulation carrier, but to the phase difference between two consecutive symbols. As an alternative to the differential encoding it is possible to use pilot symbols during transmission, as described hereafter.
A second class of receivers consists of non-coherent receivers, that is those not requiring the information on the absolute phase of the transmitted signal. These receivers have different advantages compared to pseudocoherent receivers, namely:
1. they can be employed in situations where the synchronization recovery is difficult, such as for instance in the case of fading channels, or in presence of Doppler shift or frequency jumps due to the instability of oscillators;
2. they are simpler and cost effective since they have no PLL;
3. the synchronization state cannot be lost, contrarily to receivers with PLL where this loss can occur due to phase jumps, false locking or loss of the locking state;
4. after an out-of-duty interval caused by deep fading they are immediately operative, contrarily to receivers with PLL that require a transient period to recover the locking condition;
5. they can be employed in time division multiple access communication systems (Time Division Multiple Access, or TDMA), where coherent detection is not recommended due to the comparatively long acquisition time of the synchronism.
The first non-coherent receivers considered in technical literature were differential receivers, often employed in the detection of modulated phase digital signals, or PSK (Phase Shift Keying), where a differential coding ties the information to the phase difference between two consecutive PSK symbols. The receiver estimates this phase difference, not requiring therefore to be locked in phase with the received signal. A possible interpretation of the operation of these receivers is the following: with the differential coding process, the phase reference necessary for the data estimate is contained in the preceding symbol. Therefore it is not necessary to determine an absolute phase reference, since the preceding symbol can be used for this purpose. However, this involves a degradation of performance compared to a coherent receiver, due to the fact that in differential detection the phase reference is noisy, while in coherent detection this reference is perfectly known and therefore noise free. We could say that in the case of differential detection the signal to noise ratio (Signal-to-Noise Ratio, or SNR) of the reference signal is the same as the SNR of the information signal. In the case of a coherent receiver, on the contrary, the SNR of the reference signal is theoretically infinite. For instance, in the case of PSK modulations with two phase values only, or BPSK, (Binary PSK) the loss is small, that is 0.8 dB approximately at bit error rate, or BER, (Bit Error Rate) of 10xe2x88x925. On the contrary, in the case of PSK modulations with M  greater than 2 phase values, or M-PSK, the performance loss can reach 3 dB. Starting from the above considerations, differential receivers have been conceived, drawing the phase reference from a given number of past symbols, in order to xe2x80x9cfilterxe2x80x9d the noise effect. In this way the SNR of the phase reference is of higher quality and the performance approaches that of a coherent receiver. This type of receivers employing a so-called xe2x80x9cdecision feedbackxe2x80x9d are described, for instance in the following papers:
xe2x80x9cThe phase of a vector perturbed by Gaussian noise and differentially coherent receiversxe2x80x9d, authors: H. Leib, S. Pasupathy, published in IEEE Trans. Inform. Theory, vol. 34, pp.1491-1501, November 1988.
xe2x80x9cBit error rate of binary and quaternary DPSK signals with multiple differential feedback detectionxe2x80x9d, author: F. Edbauer, published in IEEE Trans. Commun., vol. 40, pp. 457-460, March 1992.
They can be considered the forerunners of block differential receivers, or N-differential receivers, described below.
Block differential receivers fill the performance gap between coherent performance and simple differential ones, and are well described in the following papers:
xe2x80x9cMulti-symbol detection of M-DPSKxe2x80x9d, authors: G. Wilson, J. Freebersyser and C. Marshall, published in the Proceedings of IEEE GLOBECOM, pp.1692-1697, November 1989;
xe2x80x9cMultiple-symbol differential detection of MPSKxe2x80x9d, authors: D. Divsalar and M. K. Simon, published in IEEE Trans. Commun., vol. 38, pp.300-308, March 1990;
xe2x80x9cNon-coherent block demodulation of PSKxe2x80x9d, authors: H. Leib, S. Pasupathy, published in the Proceedings of IEEE VTC, pp.407-411, May 1990;
and in the volume under the title xe2x80x9cDigital communication techniquesxe2x80x9d, authors: M. K. Simon, S. M. Hinedi and W. C. Lindsey, published by Prentice Hall, Englewood Cliffs, 1995, for the case of M-PSK modulations.
Block differential receivers, as well as those adopting decision feedback, are based on the idea of extending the observation interval on which decisions are based, compared to the observation interval of two symbols only, typical of simple differential receivers. For the latter, there is an additional peculiarity, which is deciding on multiple symbols at the same time, instead of symbol by symbol. N-differential receivers use an observation window of N symbols, and simultaneously make the decision on N-1 information symbols. This decision strategy can be seen as an extension of the decision strategy of differential receivers, which in fact correspond to case N=2. It has been demonstrated that in the case of M-PSK modulations, for Nxe2x86x92+∞ the performance of this type of receiver tends to be like that of the coherent receiver. A number of examples of block differential receivers can be found in the literature, suitable to the different modulations; some of which are described in the papers mentioned above. In addition, we point out that:
M-PSK modulations with channel coding are described in the paper under the title xe2x80x9cThe performance of trellis-coded MDPSK with multiple symbol detectionxe2x80x9d, authors: D. Divsalar, M. K. Simon and M. Shahshahani, published in IEEE Trans. Commun., vol. 38, pp.1391-1403, September 1990;
M-QAM coded and uncoded modulations (Quadrant Amplitude Modulation) are addressed in the paper xe2x80x9cMaximum-likelihood differential detection of uncoded and trellis coded amplitude phase modulation over AWGN and fading channels metrics and performancexe2x80x9d, authors: D. Divsalar and M. K. Simon, published in IEEE Trans. Commun., vol. 42, pp.76-89, January 1994;
M-PSK and M-QAM modulations in fading channels, are treated in the previous article and in the article under the title xe2x80x9cOptimal decoding of coded PSK and QAM signals in correlated fast fading channels and AWGN: a combined envelope, multiple differential and coherent detection approachxe2x80x9d, authors: D. Makrakis, P. T. Mathiopoulos and D. P. Bouras, published in IEEE Trans. Commun., vol. 42, pp.63-75, January 1994.
Some disadvantages, common to all the block differential or N-differential receivers, described in the extensive literature mentioned above, are caused by the type of strategy used in the decision, consisting of an exhaustive search made on the single data blocks. Therefore it is necessary to use small values of N, otherwise calculations would be exceedingly complicated even for small sizes of the input alphabet, practically impairing the realization of the receivers. To overcome this difficulty, those skilled in the art could think to estimate the transmitted sequence using the Viterbi algorithm, but would soon conclude that this way is not practicable since the metric can be made recurrent in none of the described receivers. In light of the above, some N-differential receivers are known, employing, though inappropriately, the Viterbi algorithm. In the case of M-PSK modulations, these receivers have been described in the following articles:
xe2x80x9cNon-coherent coded modulationxe2x80x9d, author: D. Raphaeli, published in IEEE Trans. Commun., vol. 44, pp.172-183, February 1996;
xe2x80x9cA Viterbi-type algorithm for efficient estimation of M-PSK sequences over the Gaussian channel with unknown carrier phasexe2x80x9d, authors: P. Y. Kam and P. Sinha, published in IEEE Trans. Commun., vol. 43, pp.2429-2433, September 1995.
Non-coherent receivers described by D. Raphaeli, representing the more pertinent known art, are based on maximally overlapped observations, that is extended to N-1 symbols preceding the present one, assumed as independent, even if they are not in reality, as the author clearly admits. We can also observe that the metrics used are identical to those heuristically assigned to the most recent symbols in the receivers described by P. Y. Kam and P. Sinha, where decisions are locally made, at each node of a trellis diagram. In this case there is no accumulation of metrics as, on the contrary, it occurs in the classical Viterbi algorithm. The interesting thing to be noticed in the receivers described by D. Raphaeli is that they reach a good operation performance, though inappropriately using the Viterbi algorithm. The approximation introduced, consists in recurrently having, the metrics of the previous N-differential block receivers for the sole purpose of employing the Viterbi algorithm, but without basing the assumptions on metrics and their use in the algorithm context, on effective and convincing theoretical postulates, justifying this recurrence relation. The performance of these receivers, while good, finds however a limit in the approximation introduced.
Therefore an object of the present invention is to further improve the performance of known non-coherent receivers, at equal or reduced complexity level, at equal performance, and to indicate a non-coherent reception procedure of coded symbol sequences transmitted on a communication channel, affected by additive white gaussian noise, based on a more effective use of the Viterbi algorithm for the maximum likelihood estimation of the transmitted sequence. A receiver is also disclosed, performing the above mentioned procedure.
To attain these objects, an embodiment of the present invention is a non- coherent reception procedure of coded symbol sequences, obtained by amplitude and/or phase digital modulation of a carrier, transmitted on a communication channel, affected by additive white gaussian noise, based on the use of the Viterbi algorithm applied to a trellis sequence diagram, or trellis, where the branches represent all possible transitions among states defined by all possible subsequences of information symbols, possibly encoded, of finite length, through which algorithm paths are selected at each symbol interval on the trellis such that a path metric, cumulative of transition metrics, is maximum, the path metric being an indication of the likelihood level existing between the symbols of the path and a transmitted sequence of symbols, wherein each such transition metric is calculated through the following steps:
a) non-coherent base band conversion of the received signal, subsequent filtering of the converted signal through a filter matched to the basic pulse of the received signal, and sampling at symbol frequency of the filtered signal, obtaining a sequence of complex samples;
b) construction of a phase reference through accumulation of N-1 products among the complex sequential samples, conjugated, and corresponding code symbols, also complex, univocally associated with the relevant branch of the trellis; the number N-1 being finite length, selected in order to obtain the desired accuracy in the constructed phase, the accuracy increasing as N increases, at the expense of possible increase in the trellis complexity, expressed in terms of number of states;
c) normalization of the value of the phase reference, through division by its modulus;
d) replacement of a phase reference, or phasor, of the modulated carrier, present in the known analytical expression of the transition metrics used by an optimum coherent receiver, which could replace the non-coherent receiver whenever the phasor is known, with the phase reference constructed in the previous steps, obtaining an analytical expression for the calculation of each transition metric used by the non-coherent receiver.
In a second embodiment of the invention, the expression for calculating the trellis branch metrics is obtained from the known expression for maximum likelihood sequence estimation used by a non-coherent receiver. For this purpose, the function to maximize is interpreted as a general sequence metric, which can be obtained by recurrently updating a partial sequence metric defined at the n-th signal interval, the latter being in its turn possible to be calculated through accumulation of incremental metrics of unlimited memory. A truncation at N-1 symbols preceding the present one in the calculation of incremental metrics enables, without significant information loss, the construction of a trellis diagram to which the Viterbi algorithm can be applied for the search of the path with maximum metric, according to a known method.
A non-coherent receiver realized irrespectively of one or the other embodiments of the present invention is suitable to process both linear modulated signals, also affected by intersymbol interference, and CPM non-linear modulated ones, always giving better performance than conventional non-coherent receivers. A common inventive concept exists for the two embodiments of the invention, leading to obtain for linear modulations a common general diagram of the receiver, and in the case of M- PSK modulations, also the same analytical expressions of the branch metrics.
Like the conventional N-differential receivers, the receiver implemented according to the present invention contains a phase reconstruction memory, or a comparable one, whose length N can be selected in order to obtain a satisfactory compromise between complexity and performance. In fact, as N increases, the performance approaches that of the optimal coherent receiver (which perfectly knows the synchronism and can be implemented in practice only in an approximate way through a pseudocoherent receiver), but at the same time increases also the complexity expressed by the number of states of the trellis diagram. However, it is possible to obtain, with not too large values of N, a small complexity and nearly optimal performance. When the phase reconstruction memory of the subject receiver assumes a value equal to the length of a block in the N-differential receiver of the known art, or to the observation interval in the receiver described in the paper by D. Raphaeli of February 1996, the considered receiver exhibits better performance, because it employs an expression more effective of the branch metric, that is more compatible with the subsequent processing steps of the Viterbi algorithm and with the theoretical assumption on which the algorithm is based.
An additional aspect of the invention is a maximum likelihood sequence estimation receiver for code symbols.
Another aspect of the invention is a variant of the previous receiver valid when code symbols relate to a digital phase modulation, or M-PSK.